A263827 The number c_{Cc pi_1(B_1)}(2n) of the second amphicosm 2n-coverings over the first amphicosm.

2, 6, 10, 14, 14, 30, 18, 30, 36, 42, 26, 70, 30, 54, 70, 62, 38, 108, 42, 98, 90, 78, 50, 150, 76, 90, 116, 126, 62, 210, 66, 126, 130, 114, 126, 252, 78, 126, 150, 210, 86, 270, 90, 182, 252, 150, 98, 310, 132, 228, 190, 210, 110, 348, 182, 270, 210, 186, 122, 490, 126, 198, 324, 254, 210, 390, 138, 266, 250, 378

Offset: 1

Author

N. J. A. Sloane, Oct 28 2015

Keywords

• nonn

Links

• Gheorghe Coserea, Table of n, a(n) for n = 1..20000
• G. Chelnokov, M. Deryagina, A. Mednykh, On the Coverings of Amphicosms; Revised title: On the coverings of Euclidian manifolds B_1 and B_2, arXiv preprint arXiv:1502.01528 [math.AT], 2015.

Crossrefs

Cf. A263825-A263830, A263832.

Programs

Maple

A263827 := proc(n)
    local locn,a,twol,fourl ;
    locn := 2*n ;
    # Theorem 3 (iii)
    a := 0 ;
    for twol in numtheory[divisors](locn) do
        if type(twol,'even') then
            a := a+numtheory[sigma](locn/twol) ;
        end if;
    end do:
    for fourl in numtheory[divisors](locn) do
        if modp(fourl,4) = 0 then
            a := a-numtheory[sigma](locn/fourl) ;
        end if;
    end do:
    %*2 ;
end proc: # R. J. Mathar, Nov 03 2015

Mathematica

a[n_] := 2*Sum[If[Mod[d,4] == 2, DivisorSigma[1, 2*n/d], 0], {d, Divisors[ 2*n ] } ];
Array[a, 70] (* Jean-François Alcover, Dec 03 2017 *)

PARI

A007429(n) = sumdiv(n, d, sigma(d));
a(n) = 2*A007429(n) - if(n%2, 0, 2*A007429(n\2));
vector(70, n, a(n))  \\ Gheorghe Coserea, May 04 2016